Yudkowsky's insight, Newcomb's Paradox, "air pockets", and long and variable leads
By Scott Sumner
Saturos directed me to a comment by Eliezer Yudkowsky:
Just realized today that besides giving a real-world example of epistemic efficiency, markets also provide a real-world source of Newcomblike problems. Efficient markets can be so good at predicting you that if you raise rates today, that may cause a market reaction several years earlier.
He is referring to a paradox described as follows in Wikipedia:
A person is playing a game operated by the Predictor, an entity presented as somehow being exceptionally skilled at predicting people’s actions. The player of the game is presented with two boxes, one transparent (labeled A) and the other opaque (labeled B). The player is permitted to take the contents of both boxes, or just the opaque box B. Box A contains a visible $1,000. The contents of box B, however, are determined as follows: At some point before the start of the game, the Predictor makes a prediction as to whether the player of the game will take just box B, or both boxes. If the Predictor predicts that both boxes will be taken, then box B will contain nothing. If the Predictor predicts that only box B will be taken, then box B will contain $1,000,000.
Nozick also stipulates that if the Predictor predicts that the player will choose randomly, then box B will contain nothing.
By the time the game begins, and the player is called upon to choose which boxes to take, the prediction has already been made, and the contents of box B have already been determined. That is, box B contains either $0 or $1,000,000 before the game begins, and once the game begins even the Predictor is powerless to change the contents of the boxes. Before the game begins, the player is aware of all the rules of the game, including the two possible contents of box B, the fact that its contents are based on the Predictor’s prediction, and knowledge of the Predictor’s infallibility. The only information withheld from the player is what prediction the Predictor made, and thus what the contents of box B are.
The problem is called a paradox because two analyses that both sound intuitively logical give conflicting answers to the question of what choice maximizes the player’s payout.
At the risk of making a fool of myself, I will now resolve the Newcomb paradox. If the predictor is an extremely skilled psychologist, who is 99.999% accurate in forecasting, then you should definitely chose box A + B, since your choice doesn’t affect the amount of money in box B. If the predictor is 100% accurate, then you should just choose box B, because the act of choosing box B causes, and I emphasizes causes, the earlier prediction that you will pick box B.
That second case might bother some people, but if you think about it your annoyance with the idea of causation going back in time is actually irritation with the concept of a perfect predictor. Something most people believe is impossible. But if one did exist . . . think about it.
OK, even if you think what I just wrote is nonsense, the application to markets and monetary policy is interesting. I’ve frequently talked about “long and variable leads” in monetary policy. This was a play on the “long and variable lags” claimed by Milton Friedman, who thought that changes in the money supply had a peak impact perhaps 18 months later. I claim that changes in the money supply affect prices and output before they occur, at least in most cases. That’s because policy is at least partly forecastable, and hence (as Yudkowsky notes) asset markets (and the economy) should be impacted by expected future policy.
But here’s where things get interesting. Policymakers also care about markets, which leads to the Bernanke/Woodford circularity problem. Markets are intensely focused on every twitch in Janet Yellen’s face during Congressional testimony, and Janet Yellen is focused on what markets are doing, as an indication as to whether money is too tight. Markets are the “predictors”, and Yellen is like the person trying to win a million dollars, only in her case it’s a sound economy that is the goal (say 4% NGDP growth).
But of course the market predictor is far from perfect, and indeed is also responding to other shocks like corporate profitability, so even if it were perfect you’d need an NGDP futures market, not a stock market as a predictor. And yet it is also clear that it has some useful information. Which reminds me of this fascinating Financial Times story from a few weeks back:
“It is reasonable for investors to wonder whether Fed’s December rate hike was a policy error,” admits Bob Michele, chief investment officer of JPMorgan Asset Management. “Historically the Fed has raised rates because either growth or inflation was uncomfortably high. This time is different — growth is slow; wage growth is limited; deflation is being imported.”
Perhaps most of all, many investors now fret that they are operating without a safety net they had grown attached to during the post-financial crisis era.
Markets have been buffeted by powerful headwinds since 2008-09, ranging from predictable Middle East strife to the spectre of the disintegration of the European common currency. But central banks have been a constant source of comfort in hard times, suppressing interest rates and market volatility, thereby reinforcing the view among investors of a ‘central bank put’, or downside protection.
Such an assurance now appears less certain given the recent approach from central banks.
The Bank of Japan has failed to expand its quantitative easing programme as expected; the European Central Bank dashed unrealistically high hopes of more eurozone QE in December; the People’s Bank of China has failed to calm concerns over China through aggressive action; and the Fed has started tightening monetary policy.
As a result, the “era of asset price reflation, fuelled by both post-crisis undervaluation and aggressive central bank easing, is over”, according to Jeffrey Knight, global head of asset allocation at Columbia Threadneedle.
“It was fun while it lasted, as the recovery of financial asset prices from the nadir of the great financial crisis has been dramatic, one of history’s most fruitful periods for investors. But 2015 returns were rather different, and the early experiences of 2016 only reinforce the likelihood of a new investment climate,” he wrote in a note.
Indeed, Stephen Jen, a hedge fund manager, argues that this year’s sudden bout of concern over China has merely been the trigger for a broader reappraisal of central banking puts and omniscience by investors.
“My guess is that the new strike prices for these central bank puts are probably 10 to 20 per cent below where the markets are now,” he recently told clients. “It is the presence of this ‘air pocket’ that was the main trigger for the equity sell-off at the start of the year, in my humble opinion.”
The danger is that turbulent financial markets become a self-fulfilling prophecy by undermining confidence and weakening the global economy. That could trigger a feedback loop where turmoil hurts growth, which in turn fuels more choppiness.
Most economists maintain the risk of a US recession this year are slim, but markets are now pricing roughly even odds of one, and that in itself has consequences. . . .
Should financial turbulence infect the real economy, the US central bank’s plan to raise rates another four times this year becomes extremely challenging. Investors have long doubted this rate path, but now they are virtually laughing at it.
It may seem like market crashes cause a weaker economy, but in fact it is more likely that they predict it. Markets that crash are essentially predicting Fed failure. To make things even more complicated, the Fed uses market information in an attempt to avoid failure. A week before the FT article cited above, I wrote the following:
. . . the Fed knows that equity markets (and bond markets and commodity markets) often provide the first clue of an economy that is about to tank. Not a particularly reliable clue—recall the famous joke about the stock market predicting 11 of the past 6 recessions, but nonetheless an important clue.
Obviously the Fed can’t respond to each up and down in the market, nor should it. But here’s the problem. Because the Fed must pretend to ignore the stock market, it can’t act to correct a mistake until the carnage on Wall Street is so unmistakable that even average people think it’s necessary to step in. By that time it may be too late, a recession may already be underway.
When the FT talks about “air pockets” they are essentially talking about the extent to which central banks are willing to write off market warnings as “noise”. Beyond that point you have the famous central bank “put”. Ot at least they try to exercise a put; in 2008 they obviously failed. Fed policy seems like a stock market to monomaniacal Wall Street types, who confuse the markets with the macroeconomy. But Fed policy is actually a NGDP put exercised very clumsily by looking at noisy stock data.
The markets don’t know exactly where the central bank has set their put, so prices plunge lower and lower until they see signs from the central bank that it will boost NGDP growth. What looks like a stock crash causing an NGDP slowdown, is actually a stock market predicting that central bank passivity will fail to stop an NGDP slowdown. Markets also know that central banks prefer fed funds targeting to QE and negative IOR. And they know that central banks are “only human” and don’t like to admit mistakes by suddenly reversing course. That’s what caused the recession in 1937, and if there is one this year (still far from certain) that stubbornness will again be the cause.
The thing that has always frightened me about asset market plunges is that they already incorporate the Fed’s expected response. That should be as frightening to the Fed as the Newcomb Paradox game player contemplating the predictor’s uncanny predictive ability. You don’t just need to act; you need to do more than the market expected. Obviously that’s hard to do consistently, which means ideally you don’t want to allow NGDP expectations to plunge in the first place. In other words, “If I was headed for 4% NGDP growth, I wouldn’t start from here”.
The solution is for central banks to set up policy regimes that cause “The Predictors” to consistently predict success, i.e. to predict steady NGDP growth at 4% or 5% or whatever is the target. Did I mention NGDP futures markets?
PS. This post also relates to Paul Krugman’s famous “promise to be irresponsible” monetary stimulus at the zero bound. This idea is to promise to do something in the future that will cause the markets and the economy to behave better today. It’s called “irresponsible” because when the future actually arrives you may not want to honor that promise (economists call this ‘time inconsistency’), but if you have made it, then fear of losing your reputation leads you to honor it. Thus before Newcomb’s game begins you could promise to the predictor that you’d predict box B only. The idea is that $1,000,000 plus a good reputation for honesty is worth more than $1,001,000 and a reputation for dishonesty.
PPS. I’m in way over my head here, but doesn’t Calvinist predestination imply that by choosing to be good you cause (many decades earlier) God to select you as one of the chosen few to go to Heaven? It’s hard for me to wrap my mind around the idea that little old me could change God’s mind, but then I’m a fatalist that doesn’t believe in free will, so I guess I’ll just continue occasionally being bad. (But only in TheMoneyIllusion comment section, not this one.)
PPPS. Eliezer Yudkowsky has a wonderful introduction to market monetarist ideas, over at Facebook.
HT: Don Geddis